Question

step by step answer it❣❣​

Answer 1

$\Large{\bf{\green{\mathfrak{\dag{\underline{\underline{Given:-}}}}}}}$

• ∆ABC is a right angled at A. AD is the perpendicular to BC, AB = 5cm, BC = 13cm, AC = 12cm.

$\Large{\bf{\orange{\mathfrak{\dag{\underline{\underline{To \: Find:-}}}}}}}$

• Area of ∆ABC and length of AD

$\Large{\bf{\red{\mathfrak{\dag{\underline{\underline{Solution:-}}}}}}}$

First,

• $\sf \angle A$ = 90°

• $\implies$ AC $\perp$ AB

Now,

$\boxed{\pink{\sf Area \: of \: triangle \: = \: \dfrac{1}{2} \: * \: h \: * \: b}}$

• Here,

• h = AC = 12cm

• b = AB = 5cm

Substituting the values,

$\sf Area \: of \: triangle \: = \: \dfrac{1}{2} \: * \: AC \: * \: * \: AB$

$\sf Area \: of \: triangle \: = \: \dfrac{1}{2} \: * \: 12 \: * \: 5$

$\sf Area \: of \: triangle \: = \: \dfrac{1}{\cancel{2}} \: * \: \cancel{12} \: * \: 5$

$\sf Area \: of \: triangle \: = \: 1 \: * \: 6 \: * \: 5$

$\sf Area \: of \: triangle \: = \: 30 \: cm^{2}$

Therefore,

• Area of ∆ABC = 30cm².

Now,

• $\angle D$ = 90°

• $\implies$ AD $\perp$ BC

Now,

$\boxed{\pink{\sf Area \: of \: triangle \: = \: \dfrac{1}{2} \: * \: h \: * \: b}}$

Here,

• h = AD

• b = BC = 13cm

Substituting the values,

$\sf Area \: of \: triangle \: = \: \dfrac{1}{2} \: * \: AD \: * \: BC$

$\sf Area \: of \: triangle \: = \: \dfrac{1}{2} \: * \: AD \: * \: 13$

We know that,

• Area of ∆ABC = 30cm².

Substituting the values,

$\sf 30 \: = \: \dfrac{1}{2} \: * \: AD \: * \: 13$

$\sf 30 \: * \: 2 \: = \: AD \: * \: 13$

$\sf 60 \: = \: AD \: * \: 13$

$\sf \dfrac{60}{13} \: = \: AD$

$\sf AD \: = \: \dfrac{\cancel{60}}{\cancel{13}}$

$\sf AD \: = \: 4.6cm.$

Therefore,

• AD = 4.6cm.

Finally,

• $\underline{\boxed{\therefore{\blue{\sf Area \: of \: triangle \: = \: 30 \: cm^{2}.}}}}$

• $\underline{\boxed{\therefore{\purple{\sf AD \: = \: 4.6cm.}}}}$

Answer 2

Answer:

• 30 cm²
• 4.6 cm

Explanation:

Given

• ΔABC is a right angled at A. AD is perpendicular to BC.
• AB = 5 cm , BC = 13 cm , AC = 12 cm

To find

• Area of ΔABC
• Length of AD

Solution

↪ In ΔABC,

• BC = Hypotenuse
• AB = Base
• AC = Altitude

↪ ATP,

• AB = 5 cm
• BC = 13 cm
• AC = 12 cm

↪ Area of ΔABC,

• 1/2 × Base × Height
• 1/2 × 5cm × 12cm
• 30

↦ Area of ΔABC = 30 cm²

↪ Now, area of ΔABC,

• 1/2 × AD × BC = 30
• 1/2 × AD × 13 = 30
• AD = 60/13
• AD = 4.6

↦ Length of AD = 4.6 cm